Plaid Cymru's Rhun ap Iorwerth has been confirmed as Wales' first minister, calling it "the greatest privilege of my life".
The party leader was elected in a roll call of politicians at the Senedd's first meeting since his party's historic election victory.
Ap Iorwerth, the first non-Labour head of the Welsh government, said he was "eager to repay the trust that the people in Wales have placed in us".
Reform's Welsh leader Dan Thomas said his party would be a "robust opposition" that would hold Plaid to account.
Ap Iorwerth was officially sworn in by Mrs Justice Stacey, after a delay of several hours for the Senedd to receive a royal warrant from King Charles III.
But he told the waiting media that after waiting 100 years for his party to lead government, a few more hours "shouldn't be too much of a problem".
He's expected to appoint his government ministers on Wednesday on his first full day in office and unveil them at the Welsh government's headquarters in central Cardiff.
Speaking on the steps of the Welsh government's Cathays Park in Cardiff on Tuesday, ap Iorwerth said it was "an historic day - a shift, I hope, in the way Wales is governed".
Asked what message he would be giving Westminster now Wales has joined Scotland and Northern Ireland in having pro-independence governments, ap Iorwerth said his loyalty would "be to the people of Wales".
"I will endeavour in all I do, working constructively with the UK government, to get the best deal for Wales," he said.
He added that it would include "working with others where we have common ground across these islands".
In a speech to the Senedd after he won the vote for first minister on Tuesday, ap Iorwerth said: "Something has stirred in the soul of Wales.
"A new confidence, a new hope. A new broader horizon, never to be narrowed again.
"From this historic moment onwards every person in every part of our nation can know that the government of Wales is their government."
Ap Iorwerth promised his government would be there to "serve everyone in every community, urban and rural, old and young, whether they speak Welsh or do not".
"Where there is common ground, we will make every effort to find it," he said.
"And where unfairness and injustice threaten the fabric of our nation, we will turn that mission of kindness and tolerance into support for those who need it most."
The new expanded Senedd – with 96 MSs up from 60 – means there will 17 ministerial posts – an increase of five.
It is unclear as to whether ap Iorwerth will create any additional government posts, but Plaid has pledged to appoint a public health minister to work on preventing illness.
In the last Senedd, the key portfolios of health and finance were held by Mabon ap Gwynfor and Heledd Fychan.
Ap Iorwerth will need to think about whether giving a job to the former presiding officer Elin Jones, the only member of the 44-strong Senedd group who has ministerial experience.
In the Senedd ap Iorwerth paid tribute to former Labour first minister Eluned Morgan, saying she "steered her government with enthusiasm and with pride".
Morgan lost her seat in last week's election, as Plaid Cymru became the largest party in Cardiff Bay, winning 43 of the 96 seats.
Reform came second with 34 seats, forming the largest opposition group, while Labour shrank from 29 seats before the election to just nine.
Reform's Dan Thomas congratulated ap Iorwerth and thanked his party's Senedd members for endorsing his leadership at a group meeting on Monday.
"I wish the government well in its efforts to reduce NHS waiting lists, to improve education results, and in creating the right environment for the economy to grow and for job creation, because Wales badly needs it," he said.
He promised the Reform group would be a "robust opposition" to hold Plaid "to account" and a voice for the "left-behind communities that have voted for us".
"We represent all people across all of Wales - we all do all we can to break up the cosy consensus that has presided over 27 years of managed decline in this country."
Thomas also said there is a "pro-union majority" in the Senedd, referring to the combined number of seats won by parties opposing Welsh independence - Reform, Labour the Conservatives and Liberal Democrats, and said he will work with other pro-union parties to stop money being spent on an independence commission.
Plaid Cymru and the Greens want Wales to leave the UK.
"The future of a prosperous Wales lies within a successful United Kingdom," Thomas added.
Interim Welsh Labour leader Ken Skates told the Senedd "no one knows better than our party that it is a privilege to govern", which now "rests on different shoulders."
He paid tribute to the politicians who had lost their seats, including Eluned Morgan, who he said showed "so much dignity" for herself and for Labour.
"I do look forward to my party being an effective opposition," he said, saying Labour would be be "laser-like" in its focus on improving people's lives.
Welsh Conservative Senedd leader Darren Millar wished ap Iorwerth well, congratulating Plaid Cymru for its "formidable election result", which he said was a "huge achievement".
But he warned: "You have a monumental task before you."
"The honeymoon period for you and your party is going to be short.
"The cold reality is waiting for you in the morning," he said, referring to "an NHS which isn't working" and "a stagnant economy which isn't working".
At the Senedd, Labour's Huw Irranca-Davies was also elected the new presiding officer, or Llywydd, with Plaid's Cymru's new Senedd member Kerry Ferguson becoming his deputy.
There was a sharp change in tone in his speech stitching-up the position of presiding officer with Labour, which he said many in Wales would find unedifying.
Former Conservative Senedd group leader Paul Davies also ran for Llywydd, but was defeated by Irranca-Davies in a secret ballot.
"Frankly, it stinks," said Millar.
He said the position "should not be treated as a consolation prize for the previous deputy first minister, after their own political party has just been vomited from government in such a spectacular way by the electorate".
In response, Irranca-Davies assured Millar that he would earn the respect of everyone in the chamber through his actions as presiding officer.
Additional reporting by Adam Hale
